A094509 Numbers which are numerators of at least one reduced rational sum{k=1 to m} 1/k^n, taken over all positive integers m and n.

1, 3, 5, 9, 11, 17, 25, 33, 49, 65, 129, 137, 205, 251, 257, 363, 513, 761, 1025, 1393, 2035, 2049, 4097, 5269, 5369, 7129, 7381, 8051, 8193, 16385, 22369, 28567, 32769, 47449, 65537, 83711, 86021, 131073, 256103, 257875, 262145

Offset

1,2

Comments

It appears that the only numbers that arise twice are 1 and 49.

Links

Table of n, a(n) for n=1..41.

Example

49 is in the list since (m=3,n=2) gives 1/1^2+1/2^2+1/3^2 = 1+1/4+1/9= 49/36 and independently also since (m=6,n=1) gives 1/1+1/2+...+1/6 = 49/20

Crossrefs

Cf. A094515.

Sequence in context: A296768 A302596 A230721 * A120811 A340287 A123069

Adjacent sequences: A094506 A094507 A094508 * A094510 A094511 A094512

Keyword

nonn,frac

Author

N. J. A. Sloane, based on a suggestion of Leroy Quet, Jun 05 2004

Extensions

More terms from Hugo van der Sanden, Jun 05, 2004

The sequence of denominators could be added too. - N. J. A. Sloane.

The additional terms were calculated by Hugo van der Sanden based on the assumption that the numerator for (m=1, n=p) is always greater than that for (m=1, n<p) for all prime p - confirmation or disproof of that assumption would be helpful.

Status

approved